2 Download matlab Brownian motion model from the courseworks. Modify it to Geometric Brownian motion with starting value Xo=80, growth rate 14 = 0.09, volatility 0 = 0.22 and 5000 trajectories. Check that the code works. Try out 50,000 trajectories. Try out 100,000 trajectories. Submit the code printout and the graph printout for 5000 trajectories. % X = cumsum ( dw) ; % plot (x) ; However we resort to a slow c style code with loops for educational purposes M=5000; %number of trajectories of Brownian motion N=250; Number of steps in one trajectory X0=80; %initial point T=1; Final Time in years in trajectory dt=T/N; Stime step Sqrtdt=sqrt(dt) ; X(j , : ) j-th trajectory of Brownian Motion X(1:M, 1)=X0; % Initial value of Brownian Motion X(j, 1)=X0 for all j=1:M There index starts with 1 and not 0 as in Matlab array index should be "positive for j=1:M %generate M trajectories for i = 2:N+1 %generate j-th trajectory X(j, i)=X(j, i-1)+Sqrtdt*randn; end end t=0:dt : T; plot ( t, X ( : , : ) )